一维Kitaev模型中的逆猝灭
Reverse quenching in a one-dimensional Kitaev model
摘要：
我们提出了一个精确的结果为非绝热跃迁概率，因此在一个一维Kitaev模型的最终状态下的缺陷密度缓慢淬火的参数$J_-$，估计的各向异性之间的相互作用，作为$J_-(t)\sim -|t/τ|$。这里，时间$t$从$-\infty$变为$+\infty$，而$τ$定义了哈密尔顿算子的变化率。换句话说，最初在其基态制备的自旋链是通过在时间上线性地改变$J_-$直到量子临界点来驱动的，在这里考虑的模型中，量子临界点发生在$t=0$，反转，然后以相同的速率逐渐降低到其初始值。我们彻底比较了反向猝灭与其对应的正向猝灭$i.e.,$ $J_-\sim t/τ$。我们的精确计算表明，激发的概率为零的波矢量在瞬时能隙为零的临界点$J_{-}=0$，而不是在向前淬火的最大值的单位。它还表明，在最终状态下的缺陷密度，反向淬火，我们建议在这里，是近一半的缺陷产生的正向淬火。我们认为，当系统达到量子临界点时产生的缺陷，在反向淬火的情况下，在波矢空间中的最后一个时间重新分配，而它一直增加，直到最后一个时间的前向淬火。我们研究了逆猝灭情况下的熵密度和对角熵密度的时间演化，并与正猝灭情况进行了比较。
英文摘要：
We present an exact result for the non-adiabatic transition probability and hence the defect density in the final state of a one-dimensional Kitaev model following a slow quench of the parameter $J_-$, which estimates the anisotropy between the interactions, as $J_-(t)\sim -|t/τ|$. Here, time $t$ goes from $-\infty$ to $+\infty$ and $τ$ defines the rate of change of the Hamiltonian. In other words, the spin chain initially prepared in its ground state is driven by changing $J_-$ linearly in time up to the quantum critical point, which in the model considered here occurs at at $t=0$, reversed and then gradually decreased to its initial value at the same rate. We have thoroughly compared the reverse quenching with its counterpart forward quenching $i.e.,$ $J_-\sim t/τ$. Our exact calculation shows that the probability of excitations is zero for the wave vector at which the instantaneous energy gap is zero at the critical point $J_{-}=0$ as opposed to the maximum value of unity in the forward quenching. It is also shown that the defect density in the final state following a reverse quenching, we propose here, is nearly half of the defects generated in the forward quenching. We argue that the defects produced when the system reaches the quantum critical point gets redistributed in the wave vector space at the final time in case of reverse quenching whereas it keeps on increasing till the final time in the forward quenching. We study the entropy density and also the time evolution of the diagonal entropy density in the case of the reverse quenching and compare it with the forward case.
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